Systems which contemplate the gravitational interaction between compact objects and the matter content in a cosmological environment constitute an important problem which has been studied since the early days of General Relativity. The generalized McVittie black hole is a simple exact solution to this problem, which provides us with insight on some of its known physical aspects, as well as hints to new mechanisms which arise from a formal treatment. We review some properties of this solution and its matter source, which can be interpreted as a classical fluid but is also an exact solution to a nontrivial scalar field theory.